Question: $\vec w = (3,-2)$ $5\vec w= ($
Answer: In general, the scalar multiple of $k$ times $\vec u$ is this: $k\vec u = k(u_x, u_y) = (ku_x, ku_y)$. So, here's how we find $5 \vec{w}$ : $\begin{aligned} {5}\vec w = {5} \cdot (3,-2) &= \left({5} \cdot 3, {5} \cdot (-2)\right) \\\\ &= (15,-10) \end{aligned}$ The answer is $ (15,-10) $.